The paper studies optimal portfolio selection for discrete time market models in mean-variance and goal achieving setting. The optimal strategies are obtained for models with an observed process that causes serial correlations of price changes. The optimal strategies are found to be myopic for the goal-achieving problem and quasi-myopic for the mean variance portfolio.

Keywords: discrete time market, multi-period market, myopic strategies, serial correlation, optimal portfolio, mean variance portfolio, goal achieving

@article{COCV_2010__16_3_635_0, author = {Dokuchaev, Nikolai}, title = {Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {635--647}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, doi = {10.1051/cocv/2009008}, mrnumber = {2674630}, zbl = {1198.91185}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009008/} }

TY - JOUR AU - Dokuchaev, Nikolai TI - Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 635 EP - 647 VL - 16 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009008/ DO - 10.1051/cocv/2009008 LA - en ID - COCV_2010__16_3_635_0 ER -

%0 Journal Article %A Dokuchaev, Nikolai %T Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 635-647 %V 16 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009008/ %R 10.1051/cocv/2009008 %G en %F COCV_2010__16_3_635_0

Dokuchaev, Nikolai. Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 635-647. doi : 10.1051/cocv/2009008. http://archive.numdam.org/articles/10.1051/cocv/2009008/

[1] Dynamic portfolio strategies: quantitative methods and empirical rules for incomplete information. Kluwer, Boston (2002). | Zbl

,[2] Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation. IMA J. Management Mathematics 17 (2006) 257-276.

,[3] Discrete time market with serial correlations and optimal myopic strategies. European J. Oper. Res. 177 (2007) 1090-1104. | Zbl

,[4] Maximin investment problems for discounted and total wealth. IMA J. Management Mathematics 19 (2008) 63-74.

,[5] Optimality of myopic strategies for multi-stock discrete time market with management costs. European J. Oper. Res. (to appear). | Zbl

,[6] Optimal portfolio selection and compression in an incomplete market. Quantitative Finance 1 (2001) 336-345.

and ,[7] Regular conditional expectations of correspondences. Theory Probab. Appl. 21 (1976) 325-338. | Zbl

and ,[8] Incomplete information equilibria: separation theorem and other myths. Ann. Oper. Res. 151 (2007) 119-149. | Zbl

,[9] On optimal myopic portfolio policies, with and without serial correlation of yields. J. Bus. 44 (1971) 324-334.

,[10] Dynamic mean variance analysis. Working paper, SSRN: http://ssrn.com/abstract=323397 (2002).

,[11] Hedging general claims and optimal control. Working paper (2000).

and ,[12] Dynamic Portfolio Theory. Ph.D. Thesis, Harvard University, USA (1968).

,[13] Optimal portfolio selection: multi-period mean-variance optimization. Math. Finance 10 (2000) 387-406.

and ,[14] Quadratic hedging and mean-variance portfolio selection with random parameters in an incomplete market. Math. Oper. Res. 29 (2004) 132-161. | Zbl

,[15] Mean-variance portfolio selection with random parameters in a complete market. Math. Oper. Res. 27 (2002) 101-120. | Zbl

and ,[16] Optimization by Vector Space Methods. John Wiley, New York (1968). | Zbl

,[17] Portfolio Selection: Efficient Diversification of Investment. New York: John Wiley & Sons (1959).

,[18] Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Economics Statistics 51 (1969) 247-257.

,[19] Optimal multi-period portfolio policies. J. Business 41 (1968) 215-229.

,[20] Introduction to mathematical finance: discrete time models. Blackwell Publishers (1997).

,[21] Variance-optimal hedging in discrete time. Math. Oper. Res. 20 (1995) 1-32. | Zbl

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